Question:
If the sum of the zeros of the quadratic polynomial $k x^{2}+2 x+3 k$ is equal to the product of its zeros, then $k=?$
(a) $\frac{1}{3}$
(b) $\frac{-1}{3}$
(c) $\frac{2}{3}$
(d) $\frac{-2}{3}$
Solution:
(d) $\frac{-2}{3}$
Let $\alpha$ and $\beta$ be the zeroes of $k x^{2}+2 x+3 k$.
Then $\alpha+\beta=\frac{-2}{k}$ and $\alpha \beta=\frac{3 k}{k}=3$
$=>\alpha+\beta=\alpha \beta$
$=>\frac{-2}{k}=3$
$=>k=\frac{-2}{3}$